While only briefly considered in Section REF , a topic that is strongly related to small cut elements is explicit time integration for problems in dynamics. This is particularly interesting for crash simulations, as such problems are commonly solved by explicit time steppers [1]}. Although tools exist that result in stable time steps that are not affected by the cut elements (i.e., element aggregation, ghost penalty terms in the mass matrix, or lumping of the mass matrix [2]}, [1]}, [4]}), the research on this topic is not exhaustive. In particular, a comprehensive analysis of stable time-step sizes with different choices for the mass and stiffness forms (i.e., boundary condition enforcement technique, ghost-penalty stabilization of both forms, lumping of the mass matrix, etc.) does, to the authors' knowledge, not yet exist.
